Jared was absent today.

We'll soon have completed the data collection phase of the project. Today we worked on totting up a few more numbers, and inserting them into our Excel document. Jared, as always, does the work with Excel, and it's great to see him focused on these tasks. We're both very much looking forward to when we can start analyzing this dataset. We finished class by watching a few minutes of another video by Hans Rosling, where he again presents statistics in such a stimulating fashion.

I prefer to do Statistics with Jared when he's physically present (especially when we're working on his project!) so instead we continued with the next section in Algebra (since he was on an algebra roll!). We started looking at solving polynomial equations. The solutions can be found by identifying the intersections of the curves using a graphing calculator. First we sketched the curves of the example (x^3 + 3x^2 = x + 3) revisiting the properties of end behavior for the cubic and the slope-intercept format for the linear equation, and discussed the x-values of the intersections. We then pulled up a graphing calculator on our respective browsers, and repeated the exercise to get exact values. Tomorrow we'll catch up with Statistics.

We needed to finish off a few algebra problems from today's earlier class, so after Jared worked on them, we continued with his long-term project. I'm always impressed at how concentrated Jared is when we're working on his datasets.

We picked up where we left off in Friday talking about correlation analysis. Jared had had some thoughts over the weekend regarding correlations. He wanted to talk about an article he had in his room regarding a survey correlating car models and whether their drivers are considered good or bad. This article was rife with dubious statistical conclusions, and Jared was very aware of those! We again touched upon the subject of (formal) logic, and how important valid - and sound - logical arguments are, not only in mathematical analyses but in all walks of life.

Today we discussed various properties of datasets, and what one can do with them. There are different types of datasets, e.g. straightforward numbers as in surveys, or the behavior of celestial objects over time, or the results of medical research (control, test, placebo groups). Datasets can be characterized by the mean, for example, but this is not always an accurate representation of the global dataset. One has to analyze what the information is meant to convey before extracting certain parameters from the data. One powerful tool is correlation analysis. However, there are pitfalls that especially non-mathematically-trained people often succumb to, and that is seeing correlations where there are none. It's very important to understand the subtleties of correlation analysis.

We continued working on the data collection for Jared's project. Jared was extremely focused in this class, and was very meticulous about recording the data. In fact, he double-checked his work without any prompting from me whatsoever. We're just over halfway through with the data collection, and I can tell that Jared is very much looking forward to when he can start analyzing it.

Because Jared had started on such a roll, I decided – since he was Skypeing – that it would be more beneficial to continue with our Algebra class on dividing polynomials, rather than switch to Statistics. I had Jared work on some more problems on long division, ensuring that he was tackling them step-by-step. Apart from a few hiccups in the arithmetic, Jared worked very well indeed. Tomorrow, Statistics!

It's been a while since we worked on Jared's long-term project, so today we inserted more data points into the Excel sheets. Jared thinks we're already beginning to see a trend, so it will be very exciting once we have as large a dataset as possible to see if the possible trend holds up statistically. As always when we're working on the project, I always take the opportunity to quiz Jared on what we've already discussed regarding working in a statistically sound manner with data.

We worked on the assigned problems for Jared's homework of last night on permutations and combinations. We had covered this topic in the fall, so it was primarily a review. Jared very quickly picked up on the factorial, and completed the problems swiftly once he got going. Jared had already had a rather intense Algebra class, and had tackled the homework problems with gusto, so in view of Jared's recently expressed interest in law, to finish today's class we discussed logical fallacies and how they are (inadvertently, much of the time) introduced into arguments to favor a specific scenario, and how difficult they are to spot. This is very important in cases when medical research, for example, uses hard-fact statistics to support a study and non-scientifically-minded (often) opponents of that study counter the results using arguments that hold no logical water, but go uncontested because of a failure to spot the logical fallacies involved.